For the third time, then, I invite you to explain the error of my reasoning.
Your reasoning against a possible meta analysis and seeing statistics is
Suppose we have a number of people claiming to be able to influence the outcome of a coin toss (or to predict it, if you prefer). If we were testing this claim against chance, we would have a simple binomial problem, testing against P = .50, and we would set up a suitable number of trials. If, though, we listen to the claimants, and adjust our tests accordingly, ...
One always listens to claimants to help design the test, sure. But when it comes down to analyzing the observed data, for any test, one does something like
ztai chi = (actual hits-hits expected by chance) / stuff
and not
zmercutio = (actual hits-hits expected by what claimant says) / stuff
and one compares ztai chi, not zmercutio, to a standard normal distribution, for example, to get a probability that will help us assess the claimant's performance.
...we can save time. Let us take the extreme example in which claimants say they have complete control, and will always be able to determine the coin's face. We can test this very easily--just start flipping. There is a .5 probability that (by chance alone) any given person will fail after one toss. But that person can stop then. ...
Besides the error above, your error here is saying the person can just stop then. Surely rules will be built into such a hypothetical preliminary test to prohibit optional stopping. Both claimant and tester agree on the number of trials beforehand, this is well known. Are you really claiming that JREF or another skeptical organization, when testing a claim of a statistical nature, will agree to test someone with only one or two, or even a few trials? That is doubtful to the extreme.
Your argument seems to be with the design of the test, not meta analysis.
... The trial is over. If, on the other hand, the person got the first one right, then there is a .5 probability on the next trial (again, by chance alone). With enough claimants, we may have some people who are getting 5, or 10, or more coins called correctly before making a mistake (this all by chance alone--of course, if they *can* influence the outcome perfectly, they will never make the mistake. And yes, I recall that I am taking the extreme 100% position here, but it extrapolates to lesser claims). Now...if we take these data and combine them, they will very likely be significant. Why? Because we quit the trials earlier when they failed earlier, artificially boosting the number of successes.
I'm really not interested in "if"s and "may"s from hypothetical data from hypothetical tests being "very likely significant". Without seeing the actual data, one doesn't know if the combined data will be significant or not. That is one of the points of the exercise. One can always dream up situations for anything where something can possibly go wrong, that is not impressive. Actually seeing the data is another story.
Statistics on the table, please?
Let's start out easy: How many preliminary tests are done each year?, and How many of these tests are statistical in nature? How many of those taking the preliminary test have been tested for dowsing?
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